System and method using oam spectroscopy leveraging fractional orbital angular momentum as signature to detect materials

ABSTRACT

An apparatus that detects a material within a sample includes signal generation circuitry that generates a first signal having at least one orbital angular momentum applied thereto and applies the first signal to the sample. A detector receives the first signal after the first signal passes through the sample and detects the material responsive to a detection of a predetermined profile of orbital angular momentum states within the first signal received from the sample.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims benefit of U.S. Provisional App. No. 62/045,413,filed on Sep. 3, 2014, and entitled SYSTEM AND METHOD FOR COMMUNICATIONUSING ORBITAL ANGULAR MOMENTUM WITH MULTIPLE LAYER OVERLAY MODULATION(Atty. Dkt. No. NXGN-32335). This application is also aContinuation-in-Part of U.S. patent application Ser. No. 14/339,836,filed on Jul. 24, 2014, and entitled SYSTEM AND METHOD FOR MAKINGCONCENTRATION MEASUREMENTS WITHIN A SAMPLE MATERIAL USING ORBITALANGULAR MOMENTUM (Atty. Dkt. No. NXGN-32196). U.S. Application No.62/045,413 and Ser. No. 14/339,836 are incorporated by reference intheir entirety.

TECHNICAL FIELD

The present invention relates to a new way of spectroscopy and materialdetection of various organic and non-organic materials, and moreparticularly, to spectroscopy material detection of organic andnon-organic materials using fractional orbital angular momentum statesof waves passed through a sample of the material.

BACKGROUND

Detection of organic and non-organic materials within a sample is anincreasingly important aspect of healthcare for individuals and othertypes of monitoring systems (i.e., food, chemical, pharmaceutical,medical, and other industries). The development of non-invasivemeasurement techniques for monitoring biological and metabolic agentswithin human tissue is an important aspect of diagnosis therapy ofvarious human diseases and may play a key role in the proper managementof diseases. Examples of a biological agent that may be monitored areglucose and Beta Amyloid (responsible for Alzheimers).

Many optical techniques for sensing different materials in living tissuehave been in development over the last 50 years. These methods have beenbased upon florescent, near infrared and mid-infrared spectroscopy,Raman spectroscopy, photoacoustics, optical coherence tomography andother techniques. However, none of these techniques that have been triedhave proved completely satisfactory. Thus, an improved non-invasivetechnique enabling the detection of concentrations of various materialswithin a human body or other types of samples would have a number ofapplications within the medical field.

SUMMARY

The present invention, as disclosed and described herein, in oneembodiment thereof comprises an apparatus that detects a material withina sample includes signal generation circuitry that generates a firstsignal having at least one orbital angular momentum applied thereto andapplies the first signal to the sample. A detector receives the firstsignal after the first signal passes through the sample and detects thematerial responsive to a detection of a predetermined profile of orbitalangular momentum states within the first signal received from thesample.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding, reference is now made to thefollowing description taken in conjunction with the accompanyingDrawings in which:

FIG. 1 is a functional block diagram of a system for generating orbitalangular momentum within a signal;

FIG. 2 is a functional block diagram of the orbital angular momentumsignal processing block of FIG. 1;

FIG. 3 illustrates a single wavelength having two quanti-spinpolarizations providing an infinite number of signals having variousorbital angular momentums associated therewith;

FIG. 4A illustrates a plane wave having only variations in the spinangular momentum;

FIG. 4B illustrates a signal having both spin and orbital angularmomentum applied thereto;

FIGS. 5A-5C illustrate various signals having different orbital angularmomentum applied thereto;

FIG. 5D illustrates a propagation of Poynting vectors for various Eigenmodes;

FIG. 5E illustrates a spiral phase plate;

FIG. 6 illustrates a block diagram of an apparatus for providingconcentration measurements of various materials using orbital angularmomentum;

FIG. 7 illustrates an emitter of the system of FIG. 6;

FIG. 8 illustrates a fixed orbital angular momentum generator of thesystem of FIG. 6;

FIGS. 9A-9D illustrate various holograms for use in applying an orbitalangular momentum to a plane wave signal;

FIG. 10 illustrates the relationship between Hermite-Gaussian modes andLaguerre-Gaussian modes;

FIG. 11 illustrates super-imposed holograms for applying orbital angularmomentum to a signal;

FIG. 12 illustrates a tunable orbital angular momentum generator for usein the system of FIG. 6;

FIG. 13 illustrates a block diagram of a tunable orbital angularmomentum generator including multiple hologram images therein;

FIG. 14 illustrates the manner in which the output of the OAM generatormay be varied by applying different orbital angular momentums thereto;

FIG. 15 illustrates an alternative manner in which the OAM generator mayconvert a Hermite-Gaussian beam to a Laguerre-Gaussian beam;

FIG. 16 illustrates the manner in which holograms within an OAMgenerator may twist a beam of light;

FIG. 17 illustrates the manner in which a sample receives an OAM twistedwave and provides an output wave having a particular OAM signature;

FIG. 18 illustrates the manner in which orbital angular momentuminteracts with a molecule around its beam axis;

FIG. 19 illustrates a block diagram of the matching circuitry foramplifying a received orbital angular momentum signal;

FIG. 20 illustrates the manner in which the matching module may usenon-linear crystals in order to generate a higher order orbital angularmomentum light beam;

FIG. 21 illustrates a block diagram of an orbital angular momentumdetector and user interface;

FIG. 22 illustrates the effect of sample concentrations upon the spinangular polarization and orbital angular polarization of a light beampassing through a sample;

FIG. 23 more particularly illustrates the process that alters theorbital angular momentum polarization of a light beam passing through asample;

FIG. 24 provides a block diagram of a user interface of the system ofFIG. 6;

FIG. 25 illustrates the generation of fractional orthogonal states;

FIG. 26 illustrates the use of a spatial light modulator for thegeneration of fractional OAM beams;

FIG. 27 illustrates one manner for the generation of fractional OAM beamusing superimposed Laguerre Gaussian beams;

FIG. 28 illustrates the decomposition of a fractional OAM beam intointeger OAM states;

FIG. 29 illustrates the manner in which a spatial light modulator maygenerate a hologram for providing fractional OAM beams;

FIG. 30 illustrates the generation of a hologram to produce non-integerOAM beams;

FIG. 31 is a flow diagram illustrating the generation of a hologram forproducing non-integer OAM beams;

FIG. 32 illustrates the intensity and phase profiles for noninteger OAMbeams;

FIG. 33 is a block diagram illustrating fractional OAM beams for OAMspectroscopy analysis; and

FIG. 34 illustrates an example of an OAM state profile.

DETAILED DESCRIPTION

Referring now to the drawings, wherein like reference numbers are usedherein to designate like elements throughout, the various views andembodiments of a system and method using OAM spectroscopy leveragingfractional orbital angular momentum as signature to detect materials areillustrated and described, and other possible embodiments are described.The figures are not necessarily drawn to scale, and in some instancesthe drawings have been exaggerated and/or simplified in places forillustrative purposes only. One of ordinary skill in the art willappreciate the many possible applications and variations based on thefollowing examples of possible embodiments.

Referring now more particularly to FIG. 1, there is illustrated afunctional block diagram of a system for generating the orbital angularmomentum “twist” within a communication system. Data stream 102 isprovided to the transmission processing circuitry 100. The data stream102 is provided to the orbital angular momentum (OAM) signal processingblock 106. The modulated data stream 102 is provided an orbital angularmomentum by the orbital angular momentum electromagnetic block 106 suchthat the data stream has a unique orbital angular momentum associatedtherewith. The orbital angular momentum processed signal is provided toan optical transmitter 108 that transmits the data stream having aunique orbital angular momentum on a wavelength. Each wavelength has aselected number of bandwidth slots B and may have its data transmissioncapability increase by a factor of the number of degrees of orbitalangular momentum l that are provided from the OAM electromagnetic block106. The optical transmitter 108 transmitting signals at a singlewavelength could transmit B groups of information.

Referring now to FIG. 2, there is provided a more detailed functionaldescription of the OAM signal processing block 106. The input datastream is provided to OAM circuitry 202. The OAM circuitry 202 providesa known orbital angular momentum to the received data stream. Theorbital angular momentum is achieved by applying different currents forthe generation of the signals that are being transmitted to create aparticular orbital angular momentum associated therewith.

FIG. 3 illustrates in a manner in which a single wavelength orfrequency, having two quanti-spin polarizations may provide an infinitenumber of twists having various orbital angular momentums associatedtherewith. The l axis represents the various quantized orbital angularmomentum states which may be applied to a particular signal at aselected frequency or wavelength. The symbol omega (ω) represents thevarious frequencies to which the signals of differing orbital angularmomentum may be applied. The top grid 302 represents the potentiallyavailable signals for a left handed signal polarization, while thebottom grid 304 is for potentially available signals having right handedpolarization.

By applying different orbital angular momentum states to a signal at aparticular frequency or wavelength, a potentially infinite number ofstates may be provided at the frequency or wavelength. Thus, the stateat the frequency Δω or wavelength 306 in both the left handedpolarization plane 302 and the right handed polarization plane 304 canprovide an infinite number of signals at different orbital angularmomentum states Δl. Blocks 308 and 310 represent a particular signalhaving an orbital angular momentum Δl at a frequency Δω or wavelength inboth the right handed polarization plane 304 and left handedpolarization plane 310, respectively. By changing to a different orbitalangular momentum within the same frequency Δω or wavelength 306,different signals may also be transmitted. Each angular momentum statecorresponds to a different determined current level for transmissionfrom the optical transmitter. By estimating the equivalent current forgenerating a particular orbital angular momentum within the opticaldomain and applying this current for transmission of the signals, thetransmission of the signal may be achieved at a desired orbital angularmomentum state.

Thus, the illustration of FIG. 3, illustrates two possible angularmomentums, the spin angular momentum, and the orbital angular momentum.The spin version is manifested within the polarizations of macroscopicelectromagnetism, and has only left and right hand polarizations due toup and down spin directions. However, the orbital angular momentumindicates an infinite number of states that are quantized. The paths aremore than two and can theoretically be infinite through the quantizedorbital angular momentum levels.

Using the orbital angular momentum state of the transmitted energysignals, physical information can be embedded within the radiationtransmitted by the signals. The Maxwell-Heaviside equations can berepresented as:

${\nabla{\cdot E}} = \frac{\rho}{ɛ_{0}}$${\nabla{\times E}} = {- \frac{\partial B}{\partial t}}$ ∇⋅B = 0${\nabla{\times B}} = {{ɛ_{0}\mu_{0}\frac{\partial E}{\partial t}} + {\mu_{0\;}{j( {t,x} )}}}$

where ∇ is the del operator, E is the electric field intensity and B isthe magnetic flux density. Using these equations, one can derive 23symmetries/conserved quantities from Maxwell's original equations.However, there are only ten well-known conserved quantities and only afew of these are commercially used. Historically if Maxwell's equationswhere kept in their original quaternion forms, it would have been easierto see the symmetries/conserved quantities, but when they were modifiedto their present vectorial form by Heaviside, it became more difficultto see such inherent symmetries in Maxwell's equations.

Maxwell's linear theory is of U(1) symmetry with Abelian commutationrelations. They can be extended to higher symmetry group SU(2) form withnon-Abelian commutation relations that address global (non-local inspace) properties. The Wu-Yang and Harmuth interpretation of Maxwell'stheory implicates the existence of magnetic monopoles and magneticcharges. As far as the classical fields are concerned, these theoreticalconstructs are pseudo-particle, or instanton. The interpretation ofMaxwell's work actually departs in a significant ways from Maxwell'soriginal intention. In Maxwell's original formulation, Faraday'selectronic states (the Aμ field) was central making them compatible withYang-Mills theory (prior to Heaviside). The mathematical dynamicentities called solutions can be either classical or quantum, linear ornon-linear and describe EM waves. However, solutions are of SU(2)symmetry forms. In order for conventional interpreted classicalMaxwell's theory of U(1) symmetry to describe such entities, the theorymust be extended to SU(2) forms.

Besides the half dozen physical phenomena (that cannot be explained withconventional Maxwell's theory), the recently formulated Harmuth Ansatzalso address the incompleteness of Maxwell's theory. Harmuth amendedMaxwell's equations can be used to calculate EM signal velocitiesprovided that a magnetic current density and magnetic charge are addedwhich is consistent to Yang-Mills filed equations. Therefore, with thecorrect geometry and topology, the Aμ potentials always have physicalmeaning

The conserved quantities and the electromagnetic field can berepresented according to the conservation of system energy and theconservation of system linear momentum. Time symmetry, i.e. theconservation of system energy can be represented using Poynting'stheorem according to the equations:

$H = {{\sum\limits_{i}{m_{i}\gamma_{i}c^{2}}} + {\frac{ɛ_{0}}{2}{\int{d^{3}{x( {{E}^{2} + {c^{2}{B}^{2}}} )}\mspace{14mu} {Hamiltonian}\mspace{14mu} ( {{total}\mspace{14mu} {energy}} )}}}}$$\mspace{20mu} {{\frac{U^{mech}}{t} + \frac{U^{em}}{t} + {\oint_{s^{\prime}}{d^{2}x^{\prime}{\overset{\bigwedge}{n^{\prime}} \cdot S}}}} = {0\mspace{14mu} {conservation}\mspace{14mu} {of}\mspace{14mu} {energy}}}$

The space symmetry, i.e., the conservation of system linear momentumrepresenting the electromagnetic Doppler shift can be represented by theequations:

$\mspace{20mu} {p = {{\sum\limits_{i}{m_{i}\gamma_{i}v_{i}}} + {ɛ_{0}{\int{d^{3}{x( {E \times B} )}\mspace{14mu} {linear}\mspace{14mu} {momentum}}}}}}$${\frac{p^{mech}}{t} + \frac{p^{em}}{t} + {\oint_{s^{\prime}}{d^{2}x^{\prime}{\overset{\bigwedge}{n^{\prime}} \cdot T}}}} = {0\mspace{14mu} {conservation}\mspace{14mu} {of}\mspace{14mu} {linear}\mspace{14mu} {momentum}}$

The conservation of system center of energy is represented by theequation:

$R = {{\frac{1}{H}{\sum\limits_{i}{( {x_{i} - x_{0}} )m_{i}\gamma_{i}c^{2}}}} + {\frac{ɛ_{0}}{2H}{\int{d^{3}{x( {x - x_{0}} )}( {{E^{2}} + {c^{2}{B^{2}}}} )}}}}$

Similarly, the conservation of system angular momentum, which gives riseto the azimuthal Doppler shift is represented by the equation:

${\frac{J^{mech}}{t} + \frac{J^{em}}{t} + {\oint_{s^{\prime}}{d^{2}x^{\prime}{\overset{\bigwedge}{n^{\prime}} \cdot M}}}} = {0\mspace{14mu} {conservation}\mspace{14mu} {of}\mspace{14mu} {angular}\mspace{14mu} {momentum}}$

For radiation beams in free space, the EM field angular momentum J^(em)can be separated into two parts:

J ^(em)=ε₀∫_(V′) d ³ x′(E×A)+ε₀∫_(V′) d ³ x′E _(i)[(x′−x ₀)×∇]A _(i)

For each singular Fourier mode in real valued representation:

${J^{em} = {{{- }\frac{ɛ_{0}}{2\omega}{\int_{V^{\prime}}^{\;}{d^{3}{x^{\prime}( {E^{*} \times E} )}}}} - {\frac{ɛ_{0}}{2\omega}{\int_{V^{\prime}}^{\;}{d^{3}x^{\prime}{E_{i}\lbrack {( {x^{\prime} - x_{0}} ) \times \nabla} \rbrack}E_{i}}}}}}\ $

The first part is the EM spin angular momentum S^(em), its classicalmanifestation is wave polarization. And the second part is the EMorbital angular momentum L^(em) its classical manifestation is wavehelicity. In general, both EM linear momentum P^(em), and EM angularmomentum J^(em)=L^(em)+S^(em) are radiated all the way to the far field.

By using Poynting theorem, the optical vorticity of the signals may bedetermined according to the optical velocity equation:

${{\frac{\partial U}{\partial t} + {\nabla{\cdot S}}} = 0},\mspace{14mu} {{continuity}\mspace{14mu} {equation}}$where  S  is  the  Poynting  vector${S = {\frac{1}{4}( {{E \times H^{*}} + {E^{*} \times H}} )}},{{and}\mspace{14mu} U\mspace{14mu} {is}\mspace{14mu} {the}\mspace{14mu} {energy}\mspace{14mu} {density}}$${U = {\frac{1}{4}( {{ɛ{E}^{2}} + {\mu_{0}{H}^{2}}} )}},$

with E and H comprising the electric field and the magnetic field,respectively, and ε and μ₀ being the permittivity and the permeabilityof the medium, respectively. The optical vorticity V may then bedetermined by the curl of the optical velocity according to theequation:

$V = {{\nabla{\times v_{opt}}} = {\nabla{\times ( \frac{{E \times H^{*}} + {E^{*} \times H}}{{ɛ{E}^{2}} + {\mu_{0}{H}^{2}}} )}}}$

Referring now to FIGS. 4A and 4B, there is illustrated the manner inwhich a signal and its associated Poynting vector in a plane wavesituation. In the plane wave situation illustrated generally at 402, thetransmitted signal may take one of three configurations. When theelectric field vectors are in the same direction, a linear signal isprovided, as illustrated generally at 404. Within a circularpolarization 406, the electric field vectors rotate with the samemagnitude. Within the elliptical polarization 408, the electric fieldvectors rotate but have differing magnitudes. The Poynting vectorremains in a constant direction for the signal configuration to FIG. 4Aand always perpendicular to the electric and magnetic fields. Referringnow to FIG. 4B, when a unique orbital angular momentum is applied to asignal as described here and above, the Poynting vector S 410 willspiral about the direction of propagation of the signal. This spiral maybe varied in order to enable signals to be transmitted on the samefrequency as described herein.

FIGS. 5A through 5C illustrate the differences in signals havingdifferent helicity (i.e., orbital angular momentums). Each of thespiraling Poynting vectors associated with the signals 502, 504, and 506provide a different shaped signal. Signal 502 has an orbital angularmomentum of +1, signal 504 has an orbital angular momentum of +3, andsignal 506 has an orbital angular momentum of −4. Each signal has adistinct angular momentum and associated Poynting vector enabling thesignal to be distinguished from other signals within a same frequency.This allows differing type of information to be transmitted on the samefrequency, since these signals are separately detectable and do notinterfere with each other (Eigen channels).

FIG. 5D illustrates the propagation of Poynting vectors for variousEigen modes. Each of the rings 520 represents a different Eigen mode ortwist representing a different orbital angular momentum within the samefrequency. Each of these rings 520 represents a different orthogonalchannel. Each of the Eigen modes has a Poynting vector 522 associatedtherewith.

Topological charge may be multiplexed to the frequency for either linearor circular polarization. In case of linear polarizations, topologicalcharge would be multiplexed on vertical and horizontal polarization. Incase of circular polarization, topological charge would multiplex onleft hand and right hand circular polarizations. The topological chargeis another name for the helicity index “I” or the amount of twist or OAMapplied to the signal. The helicity index may be positive or negative.

The topological charges l s can be created using Spiral Phase Plates(SPPs) as shown in FIG. 5E using a proper material with specific indexof refraction and ability to machine shop or phase mask, hologramscreated of new materials. Spiral Phase plates can transform a RF planewave (l=0) to a twisted wave of a specific helicity (i.e. l=+1).

Optical Fiber Communications

The topological charges can be created using Spiral Phase Plates (SPPs)such as that illustrated in FIG. 6E, phase mask holograms or a SpatialLight Modulator (SLM) by adjusting the voltages on SLM which createsproperly varying index of refraction resulting in twisting of the beamwith a specific topological charge. Different topological charges can becreated and muxed together and de-muxed to separate charges.

As Spiral Phase plates can transform a plane wave (l=0) to a twistedwave of a specific helicity (i.e. l=+1), Quarter Wave Plates (QWP) cantransform a linear polarization (s=0) to circular polarization (i.e.s=+1).

Concentration Measurements

Referring now to FIG. 6, there is illustrated a block diagram of theapparatus for providing concentration measurements of various materialsresponsive to the orbital angular momentum detected by the apparatus inaccordance with the principles described herein above. An emitter 602transmits wave energy 604 that comprises a series of plane waves. Theemitter 602 may provide a series of plane waves. The orbital angularmomentum generation circuitry 606 generates a series of waves having anorbital angular momentum having a known orbital angular momentum stateapplied to the waves 608 in a known manner. The orbital angular momentumgeneration circuitry 606 may utilize holograms or some other type oforbital angular momentum generation process as will be more fullydescribed herein below. The orbital angular momentum twisted waves 608are applied to a sample material 610 under test. The sample material 610contains a material, and the identification of the material isdetermined via a detection apparatus in accordance with the processdescribed herein.

A series of output waves 612 from the sample material 610 exit thesample and have a particular orbital angular momentum with a profile ofinteger or fractional OAM states imparted thereto as a result of theparticular material under study within the sample material 610. Theoutput waves 612 are applied to a matching module 614 that includes amapping aperture for amplifying a particular orbital angular momentumgenerated by the specific material under study. The matching module 614will amplify the orbital angular momentums associated with theparticular concentration of material or material type that is detectedby the apparatus. The amplified OAM waves 616 are provided to a detector618. The detector 618 detects OAM waves relating to the concentration ofa material within the sample or the profile of integer or fractional OAMstates relating to a particular material and provides this concentrationor material type information to a user interface 620. The user interface620 interprets the concentration information and provides relevantconcentration or material indication to an individual or a recordingdevice.

Referring now to FIG. 7, there is more particularly illustrated theemitter 602. The emitter 702 may emit a number of types of energy waves604 to the OAM generation module 606. The emitter 602 may emit opticalwaves 700, electromagnetic waves 702, acoustic waves 704 or any othertype of particle waves 706. The emitted waves 604 are plane waves havingno orbital angular momentum applied thereto and may come from a varietyof types of emission devices and have information included therein. Inone embodiment, the emission device may comprise a laser. Plane waveshave wavefronts that are parallel to each other having no twist orhelicity applied thereto, and the orbital angular momentum of the waveis equal to 0. The Poynting vector within a plane wave is completely inline with the direction of propagation of the wave.

The OAM generation module 606 processes the incoming plane wave 604 andimparts a known orbital angular momentum with a known state onto theplane waves 604 provided from the emitter 602. The OAM generation module606 generates twisted or helical electromagnetic, optic, acoustic orother types of particle waves from the plane waves of the emitter 602. Ahelical wave 608 is not aligned with the direction of propagation of thewave but has a procession around direction of propagation. The OAMgeneration module 606 may comprise in one embodiment a fixed orbitalangular momentum generator 802 as illustrated in FIG. 8. The fixedorbital angular momentum generator 802 receives the plane waves 604 fromthe emitter 602 and generates an output wave 804 having a fixed orbitalangular momentum with a known OAM state applied thereto.

The fixed orbital angular momentum generator 802 may in one embodimentcomprise a holographic image 803 for applying the fixed orbital angularmomentum with a known OAM state to the plane wave 604 in order togenerate the OAM twisted wave 804. Various types of holographic imagesmay be generated in order to create the desired orbital angular momentumtwist to an optical signal that is being applied to the orbital angularmomentum generator 602. Various examples of these holographic images areillustrated in FIG. 9A-9D. In one embodiment, the conversion of theplane wave signals transmitted from the emitter 602 by the orbitalangular momentum generation circuitry 706 may be achieved usingholographic images.

Most commercial lasers emit an HG₀₀ (Hermite-Gaussian) mode 1002 (FIG.10) with a planar wave front and a transverse intensity described by aGaussian function. Although a number of different methods have been usedto successfully transform an HG₀₀ Hermite-Gaussian mode 1002 into aLaguerre-Gaussian mode 1004, the simplest to understand is the use of ahologram.

The cylindrical symmetric solution u_(pl) (r,φ,z) which describesLaguerre-Gaussian beams, is given by the equation:

${u_{pl}( {r,\varphi,z} )} = {{\frac{C}{( {1 + {z^{2}/z_{R}^{2}}} )^{1/2}}\lbrack \frac{r\sqrt{w}}{w(z)} \rbrack}^{l}{L_{p}^{l}\lbrack \frac{2r^{2}}{w^{2}(z)} \rbrack}{\exp \lbrack \frac{- r^{2}}{w^{2}(z)} \rbrack}{\exp \lbrack \frac{{- }\; k\; r^{2}z}{2( {z^{2} + z_{R}^{2}} )} \rbrack}{\exp ( {{- }\; l\; \varphi} )} \times {\exp \lbrack {{( {{2p} + l + 1} )}\tan^{- 1}\frac{z}{z_{R}}} \rbrack}}$

Where z_(R) is the Rayleigh range, w(z) is the radius of the beam, L_(P)is the Laguerre polynomial, C is a constant, and the beam waist is atz=0.

In its simplest form, a computer generated hologram is produced from thecalculated interference pattern that results when the desired beamintersects the beam of a conventional laser at a small angle. Thecalculated pattern is transferred to a high resolution holographic film.When the developed hologram is placed in the original laser beam, adiffraction pattern results. The first order of which has a desiredamplitude and phase distribution. This is one manner for implementingthe OAM generation module 606. A number of examples of holographicimages for use within a OAM generation module are illustrated withrespect to FIGS. 9A-9E.

There are various levels of sophistication in hologram design. Hologramsthat comprise only black and white areas with no grayscale are referredto as binary holograms. Within binary holograms, the relativeintensities of the two interfering beams play no role and thetransmission of the hologram is set to be zero for a calculated phasedifference between zero and π, or unity for a phase difference between πand 2π. A limitation of binary holograms is that very little of theincident power ends up in the first order diffracted spot, although thiscan be partly overcome by blazing the grating. When mode purity is ofparticular importance, it is also possible to create more sophisticatedholograms where the contrast of the pattern is varied as a function ofradius such that the diffracted beam has the required radial profile.

A plane wave shining through the holographic images 902 will have apredetermined orbital angular momentum shift with a known integer orfractional OAM state profile applied thereto after passing through theholographic image 902. OAM generator 902 is fixed in the sense that asame image is used and applied to the beam being passed through theholographic image. Since the holographic image 902 does not change, thesame orbital angular momentum is always applied to the beam being passedthrough the holographic image 902. While FIG. 9A-9E illustrate a numberof embodiments of various holographic images that might be utilizedwithin the orbital angular momentum generator 602, it will be realizedthat any type of holographic image 902 may be utilized in order toachieve the desired orbital angular momentum within an beam being shinedthrough the image 902.

n another example of a holographic image illustrated in FIG. 11, thereis illustrated a hologram that utilizes two separate holograms that aregridded together to produce a rich number of orbital angular momentum(l). The superimposed holograms of FIG. 11 have an orbital angularmomentum of l=1 and l=3 which are superimposed upon each other tocompose the composite vortex grid 1102. The holograms utilized may alsobe built in a manner that the two holograms are gridded together toproduce a varied number of orbital angular momentums (l) not just on aline (l=+1, l=0, l=−1) but on a square which is able to identify themany variables more easily. Thus, in the example in FIG. 11, the orbitalangular momentums along the top edge vary from +4 to +1 to −2 and on thebottom edge from +2 to −1 to −4. Similarly, along the left edge theorbital angular momentums vary from +4 to +3 to +2 and on the right edgefrom −2 to −3 to −4. Across the horizontal center of the hologram theorbital angular momentums provided vary from +3 to 0 to −3 and along thevertical axis vary from +1 to 0 to −1. Thus, depending upon the portionof the grid a beam may pass through, varying orbital angular momentummay be achieved.

Referring now to FIG. 12, in addition to a fixed orbital angularmomentum generator, the orbital angular momentum generation circuitry606 may also comprise a tunable orbital angular momentum generatorcircuitry 1202. The tunable orbital angular momentum generator 1202receives the input plane wave 604 but additionally receives one or moretuning parameters 1204. The tuning parameters 1204 tune the tunable OAMgenerator 1202 to apply a selected orbital angular momentum with aselected OAM state so that the tuned OAM wave 1206 that is output fromthe OAM generator 1202 has a selected orbital angular momentum valuewith a known OAM state applied thereto.

This may be achieved in any number of fashions. In one embodiment,illustrated in FIG. 13, the tunable orbital angular momentum generator1202 may include multiple hologram images 1302 within the tunable OAMgenerator 1202. The tuning parameters 1204 enable selection of one ofthe holographic images 1306 in order to provide the desired OAM wavetwisted output and OAM states profile signal 1206 through a selectorcircuit 1304. Alternatively, the gridded holographic image such as thatdescribed in FIG. 11 may be utilized and the beam shined on a portion ofthe gridded image to provide the desired OAM and OAM states profileoutput. The tunable OAM generator 1202 has the advantage of beingcontrolled to apply a particular orbital angular momentum with a knownOAM state to the output orbital angular momentum wave 1206 dependingupon the provided input parameter 1204. This enables the concentrationsof a variety of different materials and differing materials to bemonitored, or alternatively, for various different concentrations of thesame material to be monitored.

Referring now to FIG. 13, there is more particularly implemented a blockdiagram of a tunable orbital angular momentum generator 1202. Thegenerator 1202 includes a plurality of holographic images 1302 forproviding orbital angular momentums and OAM states of various types to aprovided light signal. These holographic images 1302 are selectedresponsive to a selector circuitry 1304 that is responsive to the inputtuning parameters 1204. The selected filter 1306 comprises theholographic image that has been selected responsive to the selectorcontroller 1304 and receives the input plane waves 1204 to provide thetuned orbital angular momentum wave output 1206. In this manner, signalshaving a desired orbital angular momentum and OAM states may be outputfrom the OAM generation circuitry 606.

Referring now to FIG. 14, there is illustrated the manner in which theoutput of the OAM generator 606 may vary a signal by applying differentorbital angular momentum thereto. FIG. 14 illustrates helical phasefronts in which the Poynting vector is no longer parallel to the beamaxis and thus has an orbital angular momentum applied thereto. In anyfixed radius within the beam, the Poynting vector follows a spiraltrajectory around the axis. Rows are labeled by l, the orbital angularmomentum quantum number, L=l is the beams orbital angular momentum perphoton within the output signal. For each l, the left column 1402 is thelight beam's instantaneous phase. The center column 1404 comprises theangular intensity profiles and the right column 1406 illustrates whatoccurs when such a beam interferes with a plane wave and produces aspiral intensity pattern. This is illustrated for orbital angularmomentums of −1, 0, 1, 2 and 3 within the various rows of FIG. 14.

Referring now to FIG. 15, there is illustrated an alternative manner inwhich the OAM generator 606 may convert a Hermite-Gaussian beam outputfrom an emitter 602 to a Laguerre-Gaussian beams having imparted thereinan orbital angular momentum using mode converters 1504 and a Dove prism1510. The Hermite-Gaussian mode plane waves 1502 are provided to a π/2mode convertor 1504. The π/2 mode convertor 1504 produce beams in theLaguerre-Gaussian modes 1506. The Laguerre-Gaussian modes beams 1506 areapplied to either a π mode convertor 1508 or a dove prism 1510 thatreverses the mode to create a reverse Laguerre-Gaussian mode signal1512.

Referring now to FIG. 16, there is illustrated the manner in whichholograms within the OAM generator 606 generate a twisted light beam. Ahologram 1602 can produce light beam 1604 and light beam 1606 havinghelical wave fronts and associated orbital angular momentum lh perphoton. The appropriate hologram 1602 can be calculated or generatedfrom the interference pattern between the desired beam form 1604, 1606and a plane wave 1608. The resulting holographic pattern within thehologram 1602 resembles a diffraction grating, but has a l-prongeddislocation at the beam axis. When the hologram is illuminated with theplane wave 1608, the first-order diffracted beams 1604 and 1606 have thedesired helical wave fronts to provide the desired first ordereddiffracted beam display 1610.

Referring now to FIG. 17, there is more particularly illustrated themanner in which the sample 610 receives the input OAM twisted wave 608provided from the OAM generator 606 and provides an output OAM wave 612having a particular OAM signature associated therewith that depends uponthe concentration of a particular monitored material within the sample610. The sample 610 may comprise any sample that is under study and maybe in a solid form, liquid form or gas form. The sample material 610that may be detected using the system described herein may comprise avariety of different materials. As stated previously, the material maycomprise liquids such as blood, water, oil or chemicals. The varioustypes of carbon bondings such as C—H, C—O, C—P, C—S or C—N may beprovided for detection. The system may also detect various types ofbondings between carbon atoms such as a single bond (methane orIsooctane), dual bond items (butadiene and benzene) or triple bondcarbon items such as acetylene.

The sample 610 may include detectable items such as organic compoundsincluding carbohydrates, lipids (cylcerol and fatty acids), nucleicacids (C,H,O,N,P) (RNA and DNA) or various types of proteins such aspolyour of amino NH₂ and carboxyl COOH or aminos such as tryptophan,tyrosine and phenylalanine Various chains within the samples 610 mayalso be detected such as monomers, isomers and polymers. Enzymes such asATP and ADP within the samples may be detected. Substances produced orreleased by glands of the body may be in the sample and detected. Theseinclude items released by the exocrine glands via tube/ducts, endocrineglands released directly into blood samples or hormones. Various typesof glands that may have their secretions detected within a sample 610include the hypothalamus, pineal and pituitary glands, the parathyroidand thyroid and thymus, the adrenal and pancreas glands of the torso andthe hormones released by the ovaries or testes of a male or female.

The sample 610 may also be used for detecting various types ofbiochemical markers within the blood and urine of an individual such asmelanocytes and keratinocytes. The sample 610 may include various partsof the body to detect defense substances therein. For example, withrespect to the skin, the sample 610 may be used to detect carotenoids,vitamins, enzymes, b-carotene and lycopene. With respect to the eyepigment, the melanin/eumelanin, dihydroxyindole or carboxylic may bedetected. The system may also detect various types of materials withinthe body's biosynthetic pathways within the sample 610 includinghemoglobin, myoglobin, cytochromes, and porphyrin molecules such asprotoporphyrin, coporphyrin, uroporphyrin and nematoporphyrin. Thesample 610 may also contain various bacterias to be detected such aspropion bacterium, acnes. Also various types of dental plaque bacteriamay be detected such as porphyromonos gingivitis, prevotella intremediand prevotella nigrescens. The sample 610 may also be used for thedetection of glucose in insulin within a blood sample 610.

The orbital angular momentum within the beams provided within the sample2010 may be transferred from light to matter molecules depending uponthe rotation of the matter molecules. When a circularly polarized laserbeam with a helical wave front traps a molecule in an angular ring oflight around the beam axis, one can observe the transfer of both orbitaland spin angular momentum. The trapping is a form of optical tweezingaccomplished without mechanical constraints by the ring's intensitygradient. The orbital angular momentum transferred to the molecule makesit orbit around the beam axis as illustrated at 1802 of FIG. 18. Thespin angular momentum sets the molecule spinning on its own axis asillustrated at 1804.

The output OAM wave 612 from the sample 610 will have an orbital angularmomentum associated therewith that is different from the orbital angularmomentum provided on the input OAM wave 608. The difference in theoutput OAM wave 612 will depend upon the material contained within thesample 610 and the concentration of these materials within the sample610. Differing materials of differing concentration will have uniqueorbital angular momentums with a unique OAM state profile associatedtherewith. Thus, by analyzing the particular orbital angular momentumsignature associated with the output OAM wave 612, determinations may bemade as to the materials present within the sample 610 and theconcentration of these materials within the sample may also bedetermined.

Referring now to FIG. 19, the matching module 614 receives the outputorbital angular momentum wave 612 from the sample 610 that has aparticular signature associated therewith based upon the orbital angularmomentum or profile of integer or fractional OAM states imparted to thewaves passing through the sample 610. The matching module 614 amplifiesthe particular orbital angular momentum of interest in order to providean amplified wave having the desired orbital angular momentum or profileof integer or fractional OAM states of interest 616 amplified. Thematching module 614 may comprise a matching aperture that amplifies thedetection orbital angular momentum associated with a specific materialor characteristic that is under study. The matching module 614 may inone embodiment comprise a holographic filter such as that described withrespect to FIGS. 9A-9D in order to amplify the desired orbital angularmomentum wave or profile of integer or fractional OAM states ofinterest. The matching module 614 is established based upon a specificmaterial of interest that is trying to be detected by the system. Thematching module 614 may comprise a fixed module using holograms asillustrated in FIGS. 9A-9D or a tunable module in a manner similar tothat discussed with respect to the OAM generation module 606. In thiscase, a number of different orbital angular momentums could be amplifiedby the matching module in order to detect differing materials ordiffering concentration of materials within the sample 610. Otherexamples of components for the matching module 614 include the use ofquantum dots, nanomaterials or metamaterials in order to amplify anydesired orbital angular momentum values within a received wave form fromthe sample 610.

Referring now to FIG. 20, the matching module 614 rather than usingholographic images in order to amplify the desired orbital angularmomentum signals may use non-linear crystals in order to generate higherorbital angular momentum light beams. Using a non-linear crystal 2002, afirst harmonic orbital angular momentum beam 2004 may be applied to anon-linear crystal 2002. The non-linear crystal 2002 will create asecond order harmonic signal 2006.

Referring now to FIG. 21, there is more particularly illustrated thedetector 618 to which the amplified orbital angular momentum wave 616from the matching circuit 614 in order that the detector 618 may extractdesired OAM measurements 1202. The detector 618 receives the amplifiedOAM waves 616 and detects and measures observable changes within theorbital angular momentum and the profile of integer and fractional OAMstates of the emitted waves due to the concentration of a particularmaterial or the particular material under study within the sample 610.The detector 618 is able to measure observable changes within theemitted amplified OAM wave 616 from the state of the input OAM wave 608applied to the sample 610. The extracted OAM measurements 2102 areapplied to the user interface 620. The manner in which the detector 618may detect differences within the orbital angular momentum is moreparticularly illustrates with respect to FIGS. 22-23.

FIG. 22 illustrates the difference in impact between spin angularpolarization and orbital angular polarization due to passing of a beamof light through a sample 2202. In sample 2202 a, there is illustratedthe manner in which spin angular polarization is altered responsive to abeam passing through the sample 2202 a. The polarization of a wavehaving a particular spin angular momentum 2204 passing through thesample 2202 a will rotate from a position 2204 to a new position 2206.The rotation occurs within the same plane of polarization. In a similarmanner, as illustrated with respect to sample 2202 b, an image appearsas illustrated generally at 2208 before it passes through the sample2202 b. Upon passing the image through the sample 2202 b the image willrotate from the position illustrated at 2210 to a rotated positionillustrated at 2212. The amount of rotation is dependent upon the levelof concentration of the material being detected within the sample 2202.Thus, as can be seen with respect to the sample 2202 of FIG. 22, boththe spin angular polarization and the orbital angular momentum willchange based upon the concentration of materials within the sample 2202.By measuring the amount of rotation of the image caused by the change inorbital angular momentum, the concentration of a particular material maybe determined.

This overall process can be more particularly illustrated in FIG. 23. Alight source 2302 shines a light beam through expanding optics 2304. Theexpanded light beam is applied through a metalab generated hologram 2306that imparts an orbital angular momentum to the beam. The twisted beamfrom the hologram 2306 is shined through a sample 2308 having aparticular length L. This causes the generation of a twisted beam on theoutput side of the sample 2308 to create a number of detectable waveshaving various orbital angular momentums 2310 states, both integer andfractional, associated therewith. The image 2312 associated with thelight beam that is applied to sample 2308 will rotate an angle φdepending upon the concentration of the material within the sample 2308.The rotation φ of the image 2312 is different for each value orbitalangular momentum −l or +l. The change in rotation of the image Δφ may bedescribed according to the equation:

Δφ=φ₁−φ⁻¹ =f(l,L,C)

Where l is orbital angular momentum number, L is the path length of thesample and C is the concentration of the material being detected.

Thus, since the length of the sample L is known and the orbital angularmomentum may be determined using the process described herein, these twopieces of information may be able to calculate a concentration of thematerial within the provided sample.

The above equation may be utilized within the user interface moreparticularly illustrated in FIG. 24. The user interface 620 processesthe OAM measurements 2402 using an internal algorithm 2402 that providesfor the generation of concentration information 2404 that may bedisplayed in some type of user display. The algorithm would in oneembodiment utilize that equation described herein above in order todetermine the concentration based upon the length of a sample and thedetected variation in orbital angular momentum. The process forcalculating the concentration may be done in a laboratory setting wherethe information is transmitted wirelessly to the lab or the userinterface can be associated with a wearable device connected to a meteror cell phone running an application on the cell phone connected via alocal area network or wide area network to a personal or public cloud.The user interface 2420 of the device can either have a wired orwireless connection utilizing Bluetooth, ZigBee or other wirelessprotocols.

Fractional OAM Signals

Molecular spectroscopy using OAM twisted beams can leverage fractionalOAM states as a molecular signature along with other intensitysignatures (i.e. eccentricity, shift of center of mass and rotation ofthe elliptical intensity) as well as phase signatures (i.e. changes inthe phase of the scattered beam) and specific formation of publicitydistributed spectrum. The method of optical orientation of electronicsbeen by circularly polarized photons has been heavily used to study spinangular momentum in solid state materials. The process relies onspin-orbit coupling to transfer angular momentum from the spin ofprotons to the spin of electrons and has been Incorporated intopump-probe Kerr and Faraday rotation experiments to study the dynamicsof optically excited spends. By enabling the study is spin decoherence,transport and interactions, this strategy has played a role in thedevelopment of semiconductor spintronics.

The proposed spectroscopy technique focuses instead on localized orbitalangular momentum (OAM) and solids. Specifically, one can distinguishbetween delocalized OAM associated with the envelope wave function whichmay be macroscopic in spatial extent, and local OAM associated withatomic sites, which typically is incorporated into the effect of spinand associated electronic states. The former type of angular momentum isa fundamental interest to orbital fleet coherent systems, for example,quantum Hall layers, superconductors and topological insulators.Techniques to study non-equilibrium delocalized OAM in these and othersystems create opportunities to improve understanding of scattering andquantum coherence of chiral electronic states, with potentialimplications for materials discovery.

The interaction of light with glucose in beta amyloid and thespectroscopy applications of OAM with respect to these. Additionally thetransfer of OAM between acoustic and photonic modes in an ellipticalfiber, the generation of Rahman sideband carrying OAM, OAM using apleasant Monica lens, the study of optically coherent OAM in excite onsusing for wave mixing in the application of linearly polarized light tocreate a 2-D pleasant Monica analog to OAM light in patterned sinmetallic film, and the possibility of OAM light producing spin polarizedvote till electronics for efficient semiconductors may also findapplication in these techniques.

Referring now to FIG. 25, one manner for using nested fractional OAMstates to alleviate the problems associated with integer OAM states andto enable the use of stable states of fractional OAM for similarpurposes as those described herein above. In this case the input signals2502 are provided to fractional OAM generation circuitry 2504. Thefractional OAM generation circuitry 2504 generates output signals 2506having fractional orthogonal states which may then be further applied ordetected as discussed herein.

The orbital angular momentum of light beams is a consequence of theirazimuthal phase structure. Light beams have a phase factor exp(imφ),where m is an integer and φ is the azimuthal angle, and carry orbitalangular momentum (OAM) of m per photon along the beam axis. These lightbeams can be generated in the laboratory by optical devices, such asspiral phase plates or holograms, which manipulate the phase of thebeam. In cases where such a device generates an light beam with aninteger value of m, the resulting phase structure has the form of |m|intertwined helices of equal phase. For integer values of m, the chosenheight of the phase step generated by the optical device is equal to themean value of the OAM in the resulting beam.

Recently, spiral phase steps with fractional step height as well asspatial holograms have been used to generate light beams with fractionalOAM states. In these implementations, the generating optical deviceimposes a phase change of exp(iMφ) where M is not restricted to integervalues. The phase structure of such beams shows a far more complexpattern. A series of optical vortices with alternating charge is createdin a dark line across the direction of the phase discontinuity imprintedby the optical device. In order to obtain the mean value of the orbitalangular momentum of these beams, one has to average over the vortexpattern. This mean value coincides with the phase step only for theinteger and half integer values. There are certainly more connectionsbetween optics and quantum theory to represent beams with fractional OAMas quantum states.

The theoretical description of light modes with fractional OAM is basedon the generating optical device. For integer OAM values, a theoreticaldescription may exist which provides the way to treat the angle itselfas quantum mechanical Hermitian operator. The description can providethe underlying theory for a secure quantum communication system and giveform to the uncertainty relation for angle and angular momentum. Thetheory may be generalized for fractional values of M thereby creating aquantum mechanical description of fractional OAM. Such a rigorousformulation is of particular interest is the use of half integer spiralphase plates have been used to study high dimensional entanglement.Fractional OAM states are characterized not only by the height of thephase step, but also by the orientation of the phase dislocation α. Forhalf odd integer values of M, M mod l=½, states with the same M but a πdifference in a are orthogonal. In light of recent applications ofinteger OAM in quantum key distribution in the conversion of spin toorbital angular momentum in an optical medium, a rigorous formulation isimportant for possible applications of fractional OAM to quantumcommunication.

The component of the OAM in the propagation direction Lz and theazimuthal rotation angle form a pair of conjugate variables (just liketime-frequency or space-momentum). Unlike linear position and momentum,which are both defined on an unbound and continuous state space, thestate spaces for OAM and the rotation angle are different in nature. TheOAM eigenstates form a discrete set of states with m taking on allinteger values. Eigenstates of the angle operator are restricted to a 2πradian interval since it is physically impossible to distinguish betweenrotation angles differing by less than 2π radians. The properties of theangle operator are rigorously derived in an arbitrarily large, yetfinite state space of 2L+1 dimensions. This space is spanned by theangular momentum states |m

with m ranging from −L, −L+1, . . . , L. Accordingly, the 2π radianinterval [θ0, θ0+2π) is spanned by 2L+1 orthogonal angle states |θn)with θn=θ0+2πn/(2L+1). Here, θ₀ determines the starting point of theinterval and with it a particular angle operator φ̂θ. Only after physicalresults have been calculated within this state space is L allowed totend to infinity, which recovers the result of an infinite but countablenumber of basis states for the OAM and a dense set of angle stateswithin a 2π radian interval.

A quantum state with fractional OAM is denoted by |M

, where M=m+μ and m is the integer part and με[0, 1) is the fractionalpart. The state |M

is decomposed in angle states according to:

${ {{{| M \rangle} = {{( {{2L} + 1} )^{- \frac{1}{2}}{\sum\limits_{n = 0}^{2L}{\exp ( {\; M\; \theta_{n}} )}}}\theta_{n}}}\rangle} \middle| M \rangle} = ( {{{2L} + {1^{- \frac{1}{2}}{\sum\limits_{n = 0}^{2L}{{\exp ( {\; m\; \theta_{n}} )}{\exp ( {\; \mu \; \theta_{n}} )}}}}}\theta_{n}}\rangle $

It is important to note that α is bounded by 0≦α<2π, so that theorientation of the discontinuity is always understood as measured fromθ₀. With this construction the fractional state |M

can be written as:

${{{{M(\alpha)}}\rangle} = {{( {{2L} + 1} )^{- \frac{1}{2}}{\exp ( {\; \mu \; \alpha} )}{\sum\limits_{n = 0}^{2L}{{\exp ( {\; M\; \theta_{n}} )}{\exp \lbrack {\; 2\pi \; \mu \; {f_{\alpha}( \theta_{n} )}} \rbrack}}}}\theta_{n}}}\rangle$

In integer based OAM generation applications light beams may begenerated using a spiral phase plate. However, light beams generatedusing a spiral phase plate with a non-integer phase step are unstable onpropagation. However, one can generate light carrying fractional orbitalangular momentum beams not with a phase step of a spiral phase plate butby a synthesis of Laguerre-Gaussian modes. This may be accomplished asillustrated in FIG. 26 using a spatial light modulator 2602. Inputsignals 2604 are provided to the spatial light modulator 2602 and usedfor the generation of fractional OAM beams 2606. The spatial lightmodulator 2602 synthesizes Laguerre Gaussian modes rather than using aphase step of a spiral phase plate. By limiting the number of Gouyphases in the superposition, one can produce a light beam from the SLM2602 which is well characterized in terms of its propagation. Thestructural stability of these fractional OAM light beams from an SLMmake them ideal for communications using fractional OAM states.Additionally as will be described herein below the beams would be usefulfor concentration measurements of various organic materials.

Using the spatial light modulator 2602, a light beam with fractional OAMmay be produced as a generic superposition of light modes with differentvalues of m. As illustrated in FIG. 27, various Laguerre-Gaussian beammodes 2702 may have a superposition process 2704 applied thereto by thespatial light modulator 2602 in order to generate the fractional beamoutputs 2706. Using the correspondence between optics and quantumtheory, OAM can be represented as a quantum state. This quantum state2802 can be decomposed into a basis of integer OAM states 2804 asgenerally illustrated in FIG. 28. The decomposition only determines theOAM index m which in a superposition of LG beams leaves the index forthe number of concentric rings unspecified. Therefore, one can make useof this flexibility to find a representation of a fractional OAM statein terms of superimposed LG beams with a minimal number of Gouy phasesto increase propagation stability. One can produce these beams using thespatial light modulator 2602 and study their propagation and vortexstructure. Light beams constructed in this manner are in excellentrealization of non-integer OAM states and are more stable on propagationand light emerging from fractional faced steps of a spiral phase plate.

Referring now to FIG. 29, there is illustrated the manner in which anSLM may be programmed to provide fractional OAM beams. Rather than usingmultiple optical elements to generate each Laguerre Gaussian modeseparately a single SLM 2902 may be programmed with a hologram 2904 thatsets the phase structure 2906 and intensity structure 2908 forgenerating the superposition. A blazed grating 2910 is also included inthe hologram 2904 to separate angularly the first fractional order. Theformula for the resulting phase distribution of the hologram 2904 andrectilinear coordinates Φ(x,y)_(holo) is given by:

Φ(x,y)_(hole)=[Φ(x,y)_(beam)+Φ(x,Λ)_(grating) mod 2π−π]sinc²[(1−l(x,y)_(beam))π]+π

In this equation Φ(x,y) beam is the phase profile of the superpositionat the beam waist for z=0 and Φ(x,Λ) grating is the phase profile of theblazed grating which depends on the period of the grating Λ. The twophase distributions are added to modulo 2π and, after subtraction of πare multiplied by an intensity mask. In regions of low intensity theintensity mask reduces the effect of the blazed grating 4610, which inturn leads to reduced intensity in the first diffraction order. Themapping between the phase depth and the desired intensity is not linearbut rather given by the trigonometric sinc function.

Referring now to FIG. 30 and FIG. 31, there are illustrated the stepsnecessary to generate a hologram for producing a non-integer OAM beam.Initially, at step 3102 a carrier phase representing a blazed grating3002 is added to the phase 3004 of the superposition modulo 2π. Thiscombined phase 3006 is multiplied at step 3104 by an intensity mask 3008which takes account of the correct mapping between the phase depth anddiffraction intensity 3010. The resulting hologram 3012 at step 3106 isa hologram containing the required phase and intensity profiles for thedesired non-integer OAM beam.

Referring now to FIG. 32, there are illustrated the intensity and phaseprofiles on propagation for a superposition of 10 modes and M=6.5.Intensity and phase profiles 3202, 3204 and 3206 show a sequence ofnumerical plots for three different propagation distances of z=0, z=2zRand z=4zR show the changes in the phase and intensity on propagationfrom the waist plane into the far field. The various cross-sections areplotted over a range of ±3w(z) for each value of z. Profiles 3208, 3210and 3212 show the corresponding experimental profiles.

The use of fractional OAM beams may be used in a number of fashions. Inone embodiment, as illustrated in FIG. 33, fractional OAM beams may begenerated from a fractional OAM beam generator 3302. These fractionalOAM beams are then shown through a sample 3304 in a manner similar tothat discussed herein above. OAM spectroscopy detection circuitry 3306may then be used to detect certain OAM fraction state profiles caused bythe OAM beam shining through the sample 3304. Particular OAM fractionstates will have a particular fractional OAM state characteristicscaused by the sample 3304. This process would work in the same manner asthat described herein above.

FIG. 34 illustrates one example of a OAM state profile that may be usedto identify a particular material within a sample. In this case, thehighest number of OAM states is illustrated at L=3. Additional statelevels are also illustrated at L=1.5; L=2.75; L=3.5 and L=4. Thisparticular OAM state profile would be uniquely associated with aparticular material and could be used to identify the material within asample when the profile was detected. The interaction of LaguerreGaussian light beams with glucose and beta amyloid have been the initialspectroscopy application of OAM to sample types.

The transfer of OAM between the acoustic and photonic modes in anoptical fiber, the generation of Raman side bands carrying OAM, OAMusing a plasmonic lens, the study of optically coherent OAM in excitonsusing four-wave mixing, the application of linearly polarized light tocreate a 2-D plasmonic analog to OAM light in a patterned thin metallicfilm and the possibility of OAM light producing spin polarizedphotoelectrons for efficient semiconductors are other potentialspectroscopy applications.

Other means of generation and detection of OAM state profiles may alsobe utilized. For example a pump-probe magneto-orbital approach may beused. In this embodiment Laguerre-Gaussian optical pump pulses impartorbital angular momentum to the electronic states of a material andsubsequent dynamics are studied with femto second time resolution. Theexcitation uses vortex modes that distribute angular momentum over amacroscopic area determined by the spot size, and the optical probestudies the chiral imbalance of vortex modes reflected off of a sample.There will be transients that evolve on timescales distinctly differentfrom population and spin relaxation but with large lifetimes.

It will be appreciated by those skilled in the art having the benefit ofthis disclosure that this system and method for using fractional orbitalangular momentum to detect materials provides an improved manner foreasily detecting materials within a sample. It should be understood thatthe drawings and detailed description herein are to be regarded in anillustrative rather than a restrictive manner, and are not intended tobe limiting to the particular forms and examples disclosed. On thecontrary, included are any further modifications, changes,rearrangements, substitutions, alternatives, design choices, andembodiments apparent to those of ordinary skill in the art, withoutdeparting from the spirit and scope hereof, as defined by the followingclaims. Thus, it is intended that the following claims be interpreted toembrace all such further modifications, changes, rearrangements,substitutions, alternatives, design choices, and embodiments.

1. An apparatus that detects a material within a sample, comprising:signal generation circuitry that generates a first signal having atleast one orbital angular momentum applied thereto and applies the firstsignal to the sample; a detector for receiving the first signal afterthe first signal passes through the sample and detecting the materialresponsive to a detection of a predetermined profile of orbital angularmomentum states within the first signal received from the sample.
 2. Theapparatus of claim 1, wherein the predetermined profile of orbitalangular momentum states further comprises a predetermined profile offractional orbital angular momentum states.
 3. The apparatus of claim 1,wherein the signal generation circuitry further comprises: an emittingsource that emits the first signal comprising a plurality of planewaves; orbital angular momentum generation circuitry that receives thefirst signal and that applies the at least one orbital angular momentumto the plane waves of the first signal.
 4. The apparatus of claim 3,wherein the orbital angular momentum generation circuitry usesLaguerre-Gaussian optical pump pulses to impart orbital angular momentumto the first signal.
 5. The apparatus of claim 4, wherein the detectorfurther uses femto second time resolution.
 6. The apparatus of claim 1,wherein the known profile of orbital angular momentum states comprises alight image defining phase structure of a series of optical vorticeswith alternating charge, a mean value of the orbital angular momentumacross the series of optical vortices comprises the orbital angularmomentum states.
 7. The apparatus of claim 1, wherein the detectorfurther determines the material based on other intensity signatureswithin the first signal, the other intensity signatures comprising atleast one of change of eccentricity, shift of center of mass androtation of elliptical intensity.
 8. The apparatus of claim 1, whereinthe detector further comprises: an orbital angular momentum detectorthat determines the profile of orbital angular momentum states of theorbital angular momentum within the first signal from the sample; and aprocessor that determines the material within the sample responsive tothe detected profile of orbital angular momentum states of the orbitalangular momentum.
 9. The apparatus of claim 7, further including a userinterface associated with the processor comprising: a set of computerinstructions that configures the processor to determine the materialwithin the sample responsive to the detected profile of orbital angularmomentum states; and a database that stores profiles of orbital angularmomentum states determined by the processor.
 10. The apparatus of claim1, wherein the detector monitors chiral imbalance of vortex modes withinthe first signal to determine the material.
 11. The apparatus of claim1, wherein differing profiles of orbital angular momentum statesindicate different materials within the sample.
 12. The apparatus ofclaim 1, wherein the predetermined profile of orbital angular momentumstates identifies delocalized orbital angular momentum within the firstsignal caused by the material in the sample.
 13. A method fordetermining a material within a sample, comprising: generating a firstsignal having at least one orbital angular momentum applied thereto;applying the first signal to the sample; receiving the first signalafter the first signal passes through the sample; detecting apredetermined profile of orbital angular momentum states within thereceived first signal; and determining the material within the samplebased on the detected predetermined profile of orbital angular momentumstates within the first signal received from the sample.
 14. The methodof claim 13, wherein the predetermined profile of orbital angularmomentum states further comprises a predetermined profile of fractionalorbital angular momentum states.
 15. The method of claim 13, wherein thestep of generating further comprises: emitting the first signalcomprising a plurality of plane waves; receiving the first signal; andapplying the at least one orbital angular momentum to the plane waves ofthe first signal.
 16. The method of claim 15, wherein the step ofapplying further comprises using Laguerre-Gaussian optical pump pulsesto impart orbital angular momentum to the first signal.
 17. The methodof claim 16, wherein the step of detection further comprises using femtosecond time resolution to detect the predetermined profile of orbitalangular momentum states.
 18. The method of claim 13, wherein the step ofdetecting the predetermined profile further comprises detecting theprofile of a light image defining phase structure of a series of opticalvortices with alternating charge, a mean value of the orbital angularmomentum across the series of optical vortices comprises the orbitalangular momentum states.
 19. The method of claim 13, wherein the step ofdetecting further comprises determining the profile of orbital angularmomentum states of the orbital angular momentum within the first signalfrom the sample.
 20. The method of claim 19, wherein the step ofdetermining further comprises determining the material within the sampleresponsive to the determined profile of orbital angular momentum statesof the orbital angular momentum.
 21. The method of claim 13, wherein thestep of detecting further comprises detecting the material based onother intensity signatures within the first signal, the other intensitysignatures comprising at least one of change of eccentricity, shift ofcenter of mass and rotation of elliptical intensity.
 22. The method ofclaim 13, wherein the step of detecting further comprises monitoring achiral imbalance of vortex modes within the first signal to detect thematerial.
 23. The method of claim 13, wherein the step of detectingfurther comprises identifying delocalized orbital angular momentumwithin the first signal caused by the material in the sample.
 24. Anapparatus that detects a material within a sample, comprising: signalgeneration circuitry that generates a first signal having at least oneorbital angular momentum applied thereto and applies the first signal tothe sample; an orbital angular momentum detector that receives the firstsignal after the first signal passes through the sample and detects aprofile of fractional orbital angular momentum states of the orbitalangular momentum within the first signal from the sample; and aprocessor that determines the material within the sample responsive tothe detected profile of fractional orbital angular momentum states ofthe orbital angular momentum.
 25. The apparatus of claim 21, wherein thesignal generation circuitry further comprises: an emitting source thatemits the first signal comprising a plurality of plane waves; orbitalangular momentum generation circuitry that receives the first signal andthat applies the at least one orbital angular momentum to the planewaves of the first signal.
 26. The apparatus of claim 23, wherein theorbital angular momentum generation circuitry further includes one of ahologram, mode sorter or phase plate that applies the at least oneorbital angular momentum having the known profile of orbital angularmomentum states to the plane waves of the first signal.
 27. Theapparatus of claim 21, further including a user interface associatedwith the processor comprising: a set of computer instructions thatconfigures the processor to determine the material within the sampleresponsive to the detected profile of orbital angular momentum states;and a database that stores profiles of orbital angular momentum statesdetermined by the processor.
 28. The apparatus of claim 21, whereindiffering profiles of orbital angular momentum states indicate differentmaterials within the sample.
 29. The apparatus of claim 24, wherein theknown profile of orbital angular momentum states comprises a light imagedefining phase structure of a series of optical vortices withalternating charge, a mean value of the orbital angular momentum acrossthe series of optical vortices comprises the orbital angular momentumstates.
 30. The apparatus of claim 24, wherein the detector furtherdetermines the material based on other intensity or phase signatureswithin the first signal, the other intensity or phase signaturescomprising at least one of change of eccentricity, shift of center ofmass and rotation of elliptical intensity.